Stochastic differential equations and applications

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systemsUseful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.

Previous edition published under title: Stochastic differential equations and their applications. 1997.

Cover; ABOUT OUR AUTHOR; STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATIONS; Copyright; DEDICATION; Preface to the Second Edition; Preface from the 1997 Edition; Contents; General Notation; 1 Brownian Motions and Stochastic Integrals; 1.1 INTRODUCTION; 1.2 BASIC NOTATIONS OF PROBABILITY THEORY; 1.3 STOCHASTIC PROCESSES; 1.4 BROWNIAN MOTIONS; 1.5 STOCHASTIC INTEGRALS; 1.6 ITO'S FORMULA; 1.7 MOMENT INEQUALITIES; 1.8 GRONWALL-TYPE INEQUALITIES; 2 Stochastic Differential Equations; 2.1 INTRODUCTION; 2.2 STOCHASTIC DIFFERENTIAL EQUATIONS; 2.3 EXISTENCE AND UNIQUENESS OF SOLUTIONS; 2.4 LP-ESTIMATES.

2.5 ALMOST SURELY ASYMPTOTIC ESTIMATES2.6 CARATHEODORY'S APPROXIMATE SOLUTIONS; 2.7 EULER-MARUYAMA'S APPROXIMATE SOLUTIONS; 2.8 SDE AND PDE: FEYNMAN-KAC'S FORMULA; 2.9 THE SOLUTIONS AS MARKOV PROCESSES; 3 Linear Stochastic Differential Equations; 3.1 INTRODUCTION; 3.2 STOCHASTIC LIOUVILLE'S FORMULA; 3.3 THE VARIATION-OF-CONSTANTS FORMULA; 3.4 CASE STUDIES; 3.5 EXAMPLES; 4 Stability of Stochastic Differential Equations; 4.1 INTRODUCTION; 4.2 STABILITY IN PROBABILITY; 4.3 ALMOST SURE EXPONENTIAL STABILITY; 4.4 MOMENT EXPONENTIAL STABILITY; 4.5 STOCHASTIC STABILIZATION AND DESTABILIZATION.

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